Potential Energy calculations requested

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pack529holycross
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Potential Energy calculations requested

Post by pack529holycross »

This is certainly going to be a challenge to answer, since there are a few variables that cannot fully be contained within the formula, but I will pose the question to the group nonetheless:

Assuming a car is well made, with optimal wheel and axle preparations, proper weight distribution and alignment, etc... if I provided the angle and length of the elevated portion of a track being built, and also probably some data on the curved section, is it POSSIBLE to provide even a rough estimate as to how FAR a 5.00 ounce PWD car could theoretically travel?


Here is the premise - Central Florida Council is going to attempt to achieve the Guiness Record for longest PWD track, currently held by the attempt in June 2010. Here is what they sent me as the pre-conditions for the attempt:

1. The track must be manufactured from materials commonly used for pinewood derby tracks.
2. In order to qualify, the track must be used in an official pinewood derby event.
3. At least one regulation derby car must make it to the finish line. If no car can complete the length of the track the attempt is invalid.


That third one has me wanting to at least forecast what our goal should be in feet, given the requirement that the term "regulation derby car" has been included. I would assume this precludes amping up the weight to provide more potential energy, so rather than try to skirt that language, I will attempt to work within the written (but vague) requirements.

SO.... ( mission impossible music playing in the background )... your mission, should you choose to accept it, is to calculate to the best of your ability, based on data provided, the potential energy of a 5.00 ounce Pinewood Derby car travelling down this (currently hypothetical) track. The baseline, as defined in the current record holder, is 263 feet, but I have no idea what the height of the incline was. I think that would be key. More to come as data is gathered.

Nicholas
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Re: Potential Energy calculations requested

Post by Rukkian »

I know this isn't what you are really looking for, but most of the really long tracks I have seen have been built with not just one big hill, but the whole length being a long gradual hill (like down an embankment). This way you do not need to build up so much speed, and potentially have the cars go flying due to excessive speed.
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Re: Potential Energy calculations requested

Post by FatSebastian »

pack529holycross wrote:is it POSSIBLE to provide even a rough estimate as to how FAR a 5.00 ounce PWD car could theoretically travel?
It may be possible to come up with a theoretical calculation. Doc Jobe sells an application VRII that performs such calculations. The program is limited to evaluating either a circular arc type track (e.g., Pinantedosi style), or inclined ramp (Besttrack style). Other factors that must be defined are things like car shape, wheel mass distribution, 3 or 4 wheels touching, effectiveness of lube (coefficient of friction between wheel and axle), and so on.

Is this post helpful? Note that a lot of assumptions much be made which could vary the outcomes, but for the given assumptions in the example the limit was just shy of 300 ft.
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Stan Pope
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Re: Potential Energy calculations requested

Post by Stan Pope »

Give me some guesses as to the starting line height and I'll apply Lastufka's sim to the problem. His sim is based on the same good theory as Jobe's and has been validated against real life test runs (which I assume Jobe's also has been.)

We can get some pretty good answers from it.

It would be good to get answers from both sims based on the same assumptions. That would give us more confidence in the possible range of answers.

I'll make assumptions about the car's aerodynamics, the bore-axle Cf, and the rear wheel weight and inertia. (I'll assume that the car will have a light front and will RR.)

Okay?
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Re: Potential Energy calculations requested

Post by pack529holycross »

While I await exact dimensions for ascending angle, distance to top of bleachers, and drop from front row to ground level, here is a photograph with the intended layout superimposed. More info as it becomes available.

Image
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Re: Potential Energy calculations requested

Post by Darin McGrew »

An interesting related calculation would be the angle of a constant-slope section of track that allows a well-made car to roll at a constant speed. That would give you an idea of how to build a record-breaking track of arbitrary length. Start with a steeper ramp to get the cars up to speed, and then let them roll down the constant-slope section of track for any distance you want.
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Re: Potential Energy calculations requested

Post by pack529holycross »

Darin McGrew wrote:An interesting related calculation would be the angle of a constant-slope section of track that allows a well-made car to roll at a constant speed. That would give you an idea of how to build a record-breaking track of arbitrary length. Start with a steeper ramp to get the cars up to speed, and then let them roll down the constant-slope section of track for any distance you want.
a few logistical issues with that path of construction - it would require alot more materials to construct, as a greater portion of the track would be higher than if the transition section was a tighter radius. inevitably there will need to be some amount of incline to avoid the opposite condition, and have the cars running UPHILL towards the 50 yard line. The field is crested in the middle so the surface is not level from midfield to end zone - yet another construction complication.
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Re: Potential Energy calculations requested

Post by Stan Pope »

Darin McGrew wrote:An interesting related calculation would be the angle of a constant-slope section of track that allows a well-made car to roll at a constant speed. That would give you an idea of how to build a record-breaking track of arbitrary length. Start with a steeper ramp to get the cars up to speed, and then let them roll down the constant-slope section of track for any distance you want.
Interesting twist, tho it may make a travesty of Guiness!

Top speed at the end of the accel. ramp is limited by head and aero losses, primarily.

Once on the "constant-slope" section, it is a balancing act between slope, bore-axle friction, rolling friction, and aero losses. If speed is kept down, then aero losses go away and the balance is between slope and bore-axle friction and rolling friction. If rear wheels are weighted and front is light, the bore-axle friction losses are less important, though rolling friction may be increased by the wheels running on their flat rather than on their edges.

Anyway, I visualize a band of rolling frictions and bore-axle frictions in which the speed of the car down the constant-slope is the main variable. Below that band, the car does not finish.

I wonder ... if the constant-slope is non-zero, is there any value to transferring weight from body to wheels? Perhaps not. And if the event is timed, lighter wheels probably go best.

To best replicate a "real race" I'd stipulate a typical track starting line height (e.g. 4') and a long flat and make it a race to the end of a long flat. Then, if need be, add ramp to get some fraction able to finish.
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Re: Potential Energy calculations requested

Post by Darin McGrew »

pack529holycross wrote:
Darin McGrew wrote:An interesting related calculation would be the angle of a constant-slope section of track that allows a well-made car to roll at a constant speed. That would give you an idea of how to build a record-breaking track of arbitrary length. Start with a steeper ramp to get the cars up to speed, and then let them roll down the constant-slope section of track for any distance you want.
a few logistical issues with that path of construction - it would require alot more materials to construct, as a greater portion of the track would be higher than if the transition section was a tighter radius. inevitably there will need to be some amount of incline to avoid the opposite condition, and have the cars running UPHILL towards the 50 yard line. The field is crested in the middle so the surface is not level from midfield to end zone - yet another construction complication.
I wasn't considering a track set up in a stadium. I was considering a track set up on a long even hill. If you have an idea of the correct slope, then you just need to find an appropriate hill. Rent (or otherwise gain access to) a lot of compatible aluminum tracks, and then connect them end-to-end.

My thought is that the slope could be tuned so that well-made cars (maintaining a relatively constant speed) finish reliably, that cars that are not made as well stall before the finish line (so use this for a district/council race?), and that extremely well-made cars might actually continue to accelerate (at least until aerodynamic drag becomes relevant).
Last edited by Darin McGrew on Mon Jan 17, 2011 3:15 pm, edited 1 time in total.
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Re: Potential Energy calculations requested

Post by pack529holycross »

Amazingly, a direct email to the architectural firm who designed the stadium was returned within hours:


Length of stands = 140’ +/-
Angle of incline = 21 degrees. Please keep in mind the seating is not a consistent angle. It changes to provide sightlines to the field from the different seating sections.
Height of first row = 5’-10”


Ok rocket scientists.... crunch those numbers!

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Re: Potential Energy calculations requested

Post by Stan Pope »

pack529holycross wrote:Amazingly, a direct email to the architectural firm who designed the stadium was returned within hours:


Length of stands = 140’ +/-
Angle of incline = 21 degrees. Please keep in mind the seating is not a consistent angle. It changes to provide sightlines to the field from the different seating sections.
Height of first row = 5’-10”


Ok rocket scientists.... crunch those numbers!

Nicholas
What? Did you use Barach's email login again?

Crown height at 50 yd line vs at base of stands?
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Re: Potential Energy calculations requested

Post by pack529holycross »

That was what I asked for in my reply email, as well as a profile drawing of the whole thing. Let us assume that it's 50% of the height at the bleachers, or about 2 ft 11" . Make it 3ft for easier calculations.
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Re: Potential Energy calculations requested

Post by pack529holycross »

Here is a variation on the question, from a different perspective.

Has anyone tested the amount of energy that is lost or would be lost if a track were constructed with an arcing left turn designed to allow the track to be longer than the longest straight measurement of your venue? An offshoot of that question is the minimum angle of decline that would permit a decent PWD car to continue to roll forward?
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Re: Potential Energy calculations requested

Post by Duane »

pack529holycross wrote:Here is a variation on the question, from a different perspective.
Has anyone tested the amount of energy that is lost or would be lost if a track were constructed with an arcing left turn designed to allow the track to be longer than the longest straight measurement of your venue?
I don't think any energy is permanently lost by a banked curve. But...
The bank angle would need to be tuned to the expected vehicle speed at that point, and this would penalize cars arriving faster or slower than that. Those cars would get turned by collisions with the guide rail rather than by solely by "vertical" forces.
The amount of lift & fall would be greater for the outside lane than for the inside lane. While the outside car is lifted higher, it is also temporarily running slower than other cars.
The total track distance is also greater for the outside lane.
So it would be very difficult to build a bent multi-lane track that is fair.
Maybe could be done by curving each lane independently as its own twisted ribbon, rather than as one wide multi-lane plane.

Some of the penalty for the outside lane could be balanced by doing a counter-turn later on the track. So the extended track would have a jog midways, rather than a permanent change in heading.

Lastly, PWD cars are not built to twist/roll quickly in the front-back axis. Doing that well would require a low angular momentum around the front-back axis, so most of the weight would be packed near the body centerline, at track level. Hard to do while also concentrating weight in the rear, and minimizing angular momentum for nose up/down motions, and minimizing air drag.

I wonder if these fairness problems would be less, if this turn were done as part of a 360-degree upside-down loop?
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